The slanted ceiling in this photo is simply the natural result of using the space in what would otherwise be unfinished attic as living space.

Any home with a roof pitch of 8:12 or better has a pretty good volume of space above the first floor in what might otherwise be the attic (I've been in a number of attics lately that I could fit my entire house inside, they were so big!).

In the room pictured above, this space under the roof has a flat gable end in the center of the photo and what appears to be a shed dormer to the right (and to the left out of the photo), creating more ceiling height and allowing that bank of windows. A structure like this will generally have to be "stick-framed", that is, built from individual large framing members as opposed to "truss-framed", built from engineered assemblies of smaller framing members.

What Houzz contributors are saying:

EW: Of course this renovation comes with an amazing bonus room. I would love to have this space as my home office.
SH:The bonus room serves as a hangout spot for the current owners' four children. The exisiting sofas, from the original living room, were recovered in a lush dark gray chennille and the rug was removed from the old bedrooms and gained a new home here. The room is above the garage and provide the girls a bit of an escape from the rest of the house.
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AFTER: Hart helped reorganize and rethink. The family really wanted a room for their children to watch TV, work on the computer and do arts and crafts in. A computer work area was put against the far wall, with a larger desk space against the wall of windows. An L-shaped living area provides separation and just the right amount of space for watching TV. The room's design renovation came from the rug, lifted from another room. The sofas were reused as well, but Hart had them re-covered and accented with nail heads.

AFTER: Hart helped reorganize and rethink. The family really wanted a room for their children to watch TV, work on the computer and do arts and crafts in. A computer work area was put against the far wall, with a larger desk space against the wall of windows. An L-shaped living area provides separation and just the right amount of space for watching TV.
The room's design renovation came from the rug, lifted from another room. The sofas were reused as well, but Hart had them re-covered and accented with nail heads.